Biharmonic integral $\mathcal{C}$-parallel submanifolds in 7-dimensional Sasakian space forms

Abstract

We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere ${\mathbb{S}}^7$ we explicitly find all 3-dimensional proper-biharmonic integral $C$-parallel submanifolds. We also determine the proper-biharmonic parallel Lagrangian submanifolds of $\mathbb{C}{P}^3$.

23 pages; minor changes and one section added

References in corpus (1)

• A short survey on biharmonic maps between Riemannian manifolds